Thing is, the sound comes from so many factors other than the bass. Innately a bass may carry some 'sound' of its own, but depending on the setup, how you play, the type of strings, the age of those strings, the amp and any processing you put on it... well, the sound changes a lot.

What's more, even players with a distinct sound, you can still recognize that it's them playing often enough because not only is their sound distinct, but they're playing is too, so it gets even more difficult to assign specific sounds to specific basses.